Discuss the continuity of function f(x)=\frac{1}{x^{3}+1} on

kdgg0909gn

kdgg0909gn

Answered question

2021-11-17

Discuss the continuity of function f(x)=1x3+1 on R

Answer & Explanation

Leory2000

Leory2000

Beginner2021-11-18Added 10 answers

Step 1
Consider the given function,
f(x)=1x3+1
The function takes indeterminate form (10), if the denominator becomes zero.
So in order to determine the points of discontinuity, equate the denominator of the rational function to zero, and solve for the roots,
x3+1=0
x3=1
x=1, i, i
Step 2
As per the given question, the analysis is limited to the set of real numbers.
So the only value of interest is x=1
Note that the function becomes undefined at point x=1, so the given function is continuous at all points except at x=1
Thus, the function is continuous in the set R{1}

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